About the Work
Vilfredo Pareto’s “New Theories of Economics” is a compact but dense methodological essay in which one of the founders of mathematical economics steps back from his own technical apparatus to explain what he believes he has been doing and why. The piece is written as a reply to critics. Several reviews of a work Pareto had recently published—his Cours d’économie politique, issued in Lausanne in two volumes—had convinced him that his readers had not fully grasped the standpoint from which the new economic theories were being advanced. Rather than answer each objection in detail, he offers a brief general exposition of the new theories themselves, so that the misunderstandings might dissolve of their own accord.
“As a matter of fact, art has always preceded science.”
The essay is deliberately impersonal in one respect and fiercely personal in another. Pareto announces at the outset that his study is purely objective: he will not attempt to assign credit among economists for the formulation of the new theories, nor to disentangle the work of predecessors from his own modest contribution. When he speaks in his own name, he explains, it is only to take responsibility for errors he may have introduced into the theories of other writers, so that no one else is blamed for his mistakes. Yet the essay is also a polemic, conducted against named critics—Professor Charles Gide, Mr. H. L. Moore—and against a whole style of reading that judges a mathematical economics by the standards of rhetorical persuasion or of practical reform.
The form of the work is that of a learned article rather than a treatise: continuous argument, illustrated by examples drawn from astronomy, mechanics, chemistry, philology, bookkeeping, and the price of corn. It moves from a defense of pure science as such, through an account of what the general equations of economic equilibrium can and cannot do, to a set of concrete rebuttals of critics and a closing statement of the questions that economic science properly sets itself. Throughout, Pareto writes as a scientist addressing other scientists, and as a man who believes that the first duty of an investigator is to be left undisturbed to follow his inquiry wherever it leads.
Context
The essay belongs to the period in which the mathematical or “Lausanne” school of economics was consolidating its position. Pareto had succeeded Léon Walras in the chair at Lausanne, and the Cours d’économie politique of 1896 was the major statement of his own system. The new theories he defends are those associated with the marginal-utility tradition: the work of Jevons, Walras, Marshall, Irving Fisher, and others who treated economic equilibrium as a system of mutually dependent quantities susceptible of mathematical expression. Pareto’s essay is thus a document of a discipline in transition, written at a moment when the mathematical method was still regarded by many economists as an eccentricity, a piece of unnecessary machinery, or an attempt to dress up truisms in the language of the calculus.
The intellectual context is also one of sharp separation between positive science and practical art. Pareto insists that economic science and economic art have different aims and different means of expression, and that confusion between them lies at the root of much criticism. He is writing against critics who measure a scientific work by its power to persuade or to console, and against reformers who expect a theory of distribution to encourage or discourage their aspirations. The essay’s repeated appeals to the example of the natural sciences—chemistry separating from physics, anatomy from chemistry, the theory of undulations in optics—show a writer determined to place economics among the experimental sciences and to accept the consequences of that placement, including the consequence that its propositions must ultimately be tested against observation.
The essay also reflects a particular institutional and personal situation. Pareto had been stung by reviews that accused him of mathematical ostentation, of grinding out truisms with expensive machinery, and of failing to reconcile the non-mathematical reader to his method. His response is not to soften the method but to explain its purpose, and to point out that a critic ought at least to have read the book he criticizes. The tone of the closing pages—impatient, ironic, occasionally scornful—belongs to a scholar who feels that he has been attacked for the wrong reasons.
Structure of the Book
The essay unfolds in three broad movements, though it is printed as a single continuous argument. The first movement is a defense of pure science and of the separation of economic questions from legal and moral ones. Pareto argues that art has always preceded science, that the two diverge as knowledge evolves, and that critics of science typically mistake its lesser immediate utility for uselessness. He illustrates the point with the example of a scholar investigating a phrase of Tacitus about ancient German land tenure, and with Voltaire’s tale of Micromegas, who must classify human activities before he can understand them. The movement concludes with the claim that economic questions have too often been conflated with legal questions, and that the time has come to separate them as chemistry and physics were once separated.
The second movement turns to the mathematical method itself. Pareto compares rational mechanics to economic theory, arguing that the theories of Jevons, Walras, Marshall, Fisher, and others give a first approximation to the full theory of economic phenomena, just as rational mechanics gives a first approximation to the concrete mechanical one. He explains that the advantage of mathematics is not greater rigor—ordinary logic can be just as rigorous—but the capacity to treat far more complicated problems than ordinary logic can generally solve. He describes Walras’s discovery of a general system of equations expressing economic equilibrium, notes his own extension of the static equations to dynamic questions, and sketches the range of results that follow: the theory of non-competing groups, international trade, comparative cost, the coefficients of production, the function of entrepreneurs, the theory of rent, the theory of crises. He then insists that the general equations rest on the hypothesis of decreasing marginal utility, and that the deductions drawn from them must be compared with experience—not to prove the facts, which cannot be demonstrated, but to test the hypotheses and the presentation.
The third movement is polemical and terminological. Pareto rebuts Mr. Moore on the relation between arithmetic and geometric progressions, quoting his own Cours on the growth of wealth in England. He argues that science would gain by developing its own terminology, as chemistry, physics, and anatomy have done, and that many criticisms of his choice of terms are of absolutely no value. He shows, with the example of a ship and its balance sheet, that whether a thing is called capital depends not on any objective quality of the thing but on the way it is used in the process of production. He dismisses the dispute over “factors of production” versus “coefficients of industry” as a quarrel about words. The essay closes by stating the questions that economic science properly asks: what are the effects of free competition, of monopoly, of a collectivist regime—questions to be treated not polemically but scientifically.
Inside the Book
The essay opens with a statement of purpose. Criticisms of the Cours d’économie politique have revealed that certain viewpoints on the new economic theories have not been thoroughly understood, and Pareto proposes a brief exposition of them. He declares the study purely objective, disclaims any intention of assigning credit among economists, and explains that when he speaks in his own name it is only to avoid making other writers responsible for errors he may have introduced into their theories.
From this preamble he moves to a general argument about the relation of art to science. Art, he says, has always preceded science. When the two drift apart in the evolution of human knowledge, critics appear asserting that science yields no useful results—criticisms largely founded on science’s less immediate utility compared with the cognate art. Art cannot confine itself to teaching; it must demonstrate persuasive power, and so it uses rhetorical devices with which science has nothing to do. Since the most persuasive reasoning is not always the soundest, economic science often differs from economic art in its means of expression: science considers expression solely for its power to disclose truth, whereas art primarily considers efficiency as persuasion. Hence economic science will not hesitate to use mathematics, philology, physiology, and the like, while art can draw on these only very limitedly, for fear of not being understood by those it must persuade.
Pareto declines to consider the general utility of pure sciences. One who believes astronomy useless, he says, should prudently not read a book on astronomy; if he enjoys such works, it would be foolish to stop at every page wishing the author had written something more valuable, such as a trade almanac. A question may legitimately be ignored or wholly put aside, but if considered at all it must be treated as fully as the science’s resources permit. He illustrates with Tacitus’s phrase about the land of the ancient Germans being occupied by the whole body of cultivators in turn and afterward divided among them according to rank. Its exact sense, he notes, has nothing to do with present human welfare; a statesman handling legislation on landed property would be justly condemned for wasting time on its meaning. Yet anyone with time and curiosity about the ancient Germans’ property system must read the principal authors on this phrase; once begun, it would be annoying to be interrupted by someone saying he wastes time, uses too much Latin, quotes Greek too often, and that ancient Germans and their land system are “not in my line.” Pareto replies that if uninterested, one should not interfere but let the interested proceed uninterrupted, investigating in every way calculated to lead to truth.
He concedes that acquiring wealth may be pleasanter than merely knowing how it is distributed. If he thought a certain book would contribute most to establishing free trade worldwide, he would devote himself to it heart and soul, setting aside pure science; one who could find means of alleviating the sufferings of the poor would have done a far greater deed than one content merely to know the exact numbers of poor and wealthy. Still, anyone pursuing such study should be left at liberty to use means enabling discovery of the law according to which incomes vary. Regarding a mathematical formula approximating this law, Professor Charles Gide says it is “endowed with no power, either of intimidating or discouraging any one of those who aspire to a greater equality of social conditions”—which Pareto equates to saying that astronomical studies will not intimidate or discourage lovers choosing a star of their own. The investigator seeking the law of wealth distribution aims neither to encourage nor to dissuade; he seeks truth. Some questions are scientifically more important than others: mechanics lets us study the movements of celestial bodies under a given law of attraction, but attention centers on movements under that law, wasting no time on irrelevant laws.
Pareto urges setting aside, once for all, discussions of science’s greater or lesser utility or persuasive power, and directing attention solely to the laws governing certain phenomena; an uninterested reader may discontinue. He recalls Voltaire’s tale of Micromegas descending to earth: to comprehend human actions, Micromegas must perceive that a large class of activities aims at providing what is useful or pleasant, another class depends on sentiment arising from mutual attraction between the sexes, and a third does not aim directly at enjoyments of sense but proceeds on sentiments called moral, religious, patriotic. To progress, Micromegas must classify activities and examine each class separately—needful in every line of study; anatomy must not be blended with chemistry, which implies no underrating of either, only that but one subject can be advantageously investigated at a time.
Economic questions, Pareto continues, have too often been construed to coincide with legal questions; the time has come to separate them, as chemistry and physics were once separated. What are the economic results of strikes? is distinct from whether laborers have the right to organize strikes; nothing is gained scientifically by not separating these very different questions. In a practical case both must be solved, but they must be solved separately if either is to be solved well.
The argument then turns to the mathematical method. Pareto compares rational mechanics to economic theory: rational mechanics gives a first approximation to the equilibrium and movements of bodies, and likewise the theories of Jevons, Walras, Marshall, Irving Fisher, and others give a first approximation to the full theory of economic phenomena. This is only an approximation, analogous to a heavy body supposed to fall in a vacuum. Pure economics can no better express the concrete economic phenomenon than rational mechanics can represent the concrete mechanical one. Here mathematics has a place: the problem of pure economics closely resembles that of rational mechanics, and since men have not succeeded in treating the latter without mathematics, it is legitimate to appeal to mathematics for the economic problem.
Many think the advantage of mathematics is greater rigor in demonstration; Pareto calls this an error, since ordinary logic can be just as rigorous. The real advantage is that mathematics lets us treat far more complicated problems than ordinary logic generally solves. Most economists insist on the mutual dependence of economic phenomena, but verbal recognition is insufficient; we must determine approximately the relations among phenomena to gain a clear conception of their interdependence. A system of equations similar to mechanics’ representation of equilibrium and movement affords this approximation, rough but better than nothing—better to know the earth is nearly round than to imagine it flat.
Professor Walras’s great contribution was discovering a general system of equations expressing economic equilibrium; Pareto admires this but entirely disagrees with Walras’s Etudes d’économie sociale, where Walras thinks economic deductions can be drawn from metaphysical principles of jurisprudence. Pareto respects but rejects this, believing only in experimental methods and demonstrations based on facts. Foremost among general problems for mathematics is the determination or indetermination of economic problems: where the number of conditions (equations) equals the number of unknown quantities, a problem is easily solved—this explains why the so-called “laws of maximum prices” contain a logical and formal impossibility.
Pareto extended the static-equilibrium equations to dynamic questions, aiming at the most accurate description of economic phenomena, and finds it remarkable that a system of equations can express both the general character and every detail of economic phenomena, binding economic theory into an integral whole. Constructing equations for homogeneous groups yields the theory of non-competing groups of Cairns, a complete theory of international trade, and a scientific interpretation of comparative cost. These formulas give coefficients of production; their variability leads to the function of entrepreneurs and to theories of different systems of production under free competition, monopoly, or a socialistic regime. Consumers reckon in marginal utility or “ophelimity,” while the entrepreneur counts in money—some criticisms might have been unnecessary had this distinction been noted. Considering the size of industrial enterprises reveals a definite maximum at which expansion stops under free competition. The general formula also addresses the distribution of savings among different uses. From the degree of facility with which savings can be turned into different species of capital, a rigorous theory of rent can be deduced. The equations show how the economic aggregate vibrates under stimulating forces; studying these vibrations leads to a theory of crises. Once the aggregate is apprehended, dividing it into exchange, production, and capitalization is arbitrary though useful; in reality these three operations are simultaneous, so synthesis must follow analysis—analogous to an astronomer’s conception of the solar system once he has the general equations of mechanics.
Since any economic phenomenon requires time, the amount of goods considered is the quantity produced and consumed in a given period; the use of capital cannot be conceived apart from time. Professor Irving Fisher developed these considerations with much ability.
The general equations of economic equilibrium rest on the hypothesis of decreasing marginal utility, so we must ask whether they yield results borne out by experience—the only adequate demonstration of political economy’s propositions. The first part of the argument only draws conclusions from hypotheses and says nothing of their validity as concrete facts; deductions must be compared with experience for two purposes: definitive proof of hypotheses, otherwise only a priori probable, and a test of whether this presentation exhibits the substantial bearing of the phenomena. For instance, experience teaches that the quantity of goods demanded decreases with increased price; do the general equations lead to this conclusion theoretically? If yes, the grounds for accepting them strengthen; if no, they must be rejected. Many critics of the Cours misunderstood this, erroneously imagining that comparing deductions with facts was meant to prove the facts. But a fact cannot be demonstrated—it must be observed, then used to test a deduction. Even the simplest facts serve such verification. From failing to appreciate this, critics made remarks such as: “After a long deduction from a formula he states that the truthfulness of that which is deduced can be seen at once from simpler considerations. Such overfondness for mathematical machinery strengthens the impression that exists among many that this machinery is capable only of grinding out truisms.” Similar remarks could be made about light-interference discussions based on light-vibration equations; but the theory of undulations cannot demonstrate interference—rather, the phenomena ground the theory’s acceptance. Likewise, the general equations do not demonstrate the law of supply and demand; rather, equations representing the chief phenomena of supply and demand are proven by experience. There is no truism here. A calculating machine’s accuracy might be tested by multiplying 15 by 12 and comparing with the usual method, but this verification is not a demonstration, nor should one say an expensive machine was built solely to multiply 15 by 12. Another writer, Mr. H. L. Moore, repeats the objection nearly verbatim, saying that after the complex development Pareto points out that substantially the same results might be obtained without the use of differential calculus, and that Pareto cannot expect to reconcile his non-mathematical reader by telling him that if he does not understand the mathematical explanations he will have all the advantage in learning the language in which they are written.
The final movement opens with a direct rebuttal of Moore on the relationship between arithmetic and geometric progressions. Pareto argues that one can always construct an arithmetic progression whose terms, within given limits, exceed those of a given geometric progression. He characterizes his critic’s complex argument as equivalent to the proposition that within given limits the ordinates of a straight line will be larger than those of a given curve. He directs readers dissatisfied with Moore’s assertion to his own Cours, Volume I, page 341, where he gives the expression for gross income in England: R = 346.30 × 10^(0.01104t). He also quotes a passage explaining that the ratio of this progression is much more rapid than that found for population increase, which explains how wealth per inhabitant has increased considerably. Pareto states that in his text he observed that in England wealth has grown more rapidly than population, and in his notes he furnished the precise expression for the geometric progression followed by the growth of wealth. He asks whether it is not “a curious slip” for a critic to have missed this, explaining that the reason the explanation is in the notes is that it could not be given without mathematics, and he desired to keep mathematics out of the text. He concludes that it should not be deemed unnecessary to read a book one attempts to criticise.
Pareto then argues that science would gain by developing its own terminology, as chemistry, physics, and anatomy have done. In this transition period, many judge works written according to new methods as if written according to past principles. Consequently, criticisms he considers of absolutely no value have been made upon the terminology he chose in his Cours. For instance, he adopted Professor Walras’s definition of capital but deduced no conclusions from it. If anyone prefers a different definition, there would be no objection, and he would obtain the same results if he reasoned exclusively about things and not about words alone. Pareto ventures that he could rewrite his whole Cours and obtain the same results without even mentioning the term “capital,” if it were worth the while. The base of calculations regarding production is the budget of the producer. He gives an example: a person owned a ship costing £2000 on January 1, 1895; its value decreased to £1800 by January 1, 1896. During 1895 the person expended £1000 and received £4100 for hire of the vessel. These facts must be gathered from his budget, whatever form it appears in. The equations of production only formulate facts of a similar character. Among the various forms a balance sheet can assume, one is particularly suitable for certain theoretical deductions. Suppose we put the vessel down for £2000, its value on January 1, 1895. As the ship is now worth only £1800, we are obliged to charge £200 to expenses so as not to violate the form of the budget. Since we know the vessel has the same value on January 1, 1895 as on January 1 of the following year, we may eliminate it altogether from the balance. The vessel figures in our business only because it rendered us a certain amount of “services” during 1895. This method of bookkeeping may be used for many other things. As it is convenient to designate these things by a name, let us call them “capitals.” Let us refrain from thinking that in giving them a name we change their nature, and not waste time discussing the name. If anyone prefers a different name, he is free to adopt it. If it should be found convenient to state the budget in some other form, we need not hesitate, as results will doubtless be the same. The very same thing can be considered as capital or not as capital, according to our way of looking at it when we draw up the balance sheet of production. To be capital is not to possess an objective quality analogous to specific weight or chemical constitution; it is a characteristic which depends upon the way we use a thing in the process of production.
Another perfectly valueless discussion is whether it is preferable to use the term “factors of production” or “coefficients of industry.” Pareto supposes four hectares are needed to produce eighty hectolitres of corn. These four hectares are called “factors of production” of the corn. Professor Walras takes as a premise the quantity of ground needed to give a unit of produce. In the case assumed, four-eightieths or one-twentieth of a hectare is required to raise one hectolitre of corn. Walras gives to this one-twentieth of a hectare the name “coefficient of industry.” Pareto asks whether it does not amount to the same thing to say that four hectares yield eighty hectolitres of corn, or that one-twentieth of a hectare yields one hectolitre of corn. One must be overfond of disputing about words to drift into endless discussions as to the best term for presenting any given fact. He mentions many other discussions of the same character, all similarly wanting in simple common sense, but prefers to drop the subject and pass to more serious questions.
Pareto states that the presentation of the economic phenomenon in its entirety affords a clear comprehension of the effects of all conceivable economic organizations concerned, but this knowledge will always remain approximate only. Science does not attempt to establish any particular method of economic organization, and it is not the business of science to do so. Science does attempt to solve problems of the following kind: what are the effects of a regime of free competition? What are those of a regime of monopoly? Those of a collectivist regime? All these questions must be treated, not from a polemical point of view, but solely as scientific questions about the consequences of given arrangements.
Main Arguments
The essay’s central argument is that economic science must be distinguished sharply from economic art, and that the new mathematical theories belong to the former. Art has always preceded science; when the two diverge, critics arise who complain that science yields no useful results, measuring it by the immediate utility of the cognate art. But science considers expression solely for its power to disclose truth, while art considers expression primarily for its efficiency as persuasion. This difference in aim explains why economic science will use mathematics, philology, physiology, and other instruments that art can employ only sparingly, for fear of losing its audience. The argument is not that science is superior to art, but that the two are different enterprises with different standards, and that judging one by the standards of the other produces only confusion.
A second argument concerns the legitimacy of pure science. Pareto refuses to debate the general utility of pure sciences, and offers instead a rule of intellectual conduct: a question may be ignored or wholly put aside, but if considered at all it must be treated as fully as the science’s resources permit. The investigator of Tacitus’s phrase about German land tenure, or of the law according to which incomes vary, is not to be interrupted by those who find the subject useless or unpleasant. The example of Gide’s remark about the mathematical formula for income distribution is used to show how absurd it is to demand that a scientific result encourage or discourage anyone; the investigator seeks truth, not consolation.
A third argument concerns the nature and purpose of the mathematical method. Mathematics is not chiefly valuable for rigor—ordinary logic can be equally rigorous—but for its capacity to handle complicated problems. The mutual dependence of economic phenomena is universally acknowledged in words, but only a system of equations can determine approximately the relations among phenomena and give a clear conception of their interdependence. Walras’s general system of equations expressing economic equilibrium is the great achievement of this approach; Pareto admires it while rejecting Walras’s attempt to draw economic deductions from metaphysical principles of jurisprudence. The determination or indetermination of economic problems—whether the number of conditions equals the number of unknown quantities—is foremost among the general problems mathematics can address, and it explains why the so-called laws of maximum prices contain a logical and formal impossibility.
A fourth argument concerns the relation of theory to experience. The general equations rest on the hypothesis of decreasing marginal utility, and the deductions drawn from them must be compared with experience. But the comparison is not a demonstration of the facts; facts cannot be demonstrated, only observed. The comparison serves to test the hypotheses, which would otherwise be only a priori probable, and to test whether the presentation exhibits the substantial bearing of the phenomena. Critics who imagine that Pareto is trying to prove the facts by deduction have misunderstood the logic of the method. The theory of undulations does not demonstrate interference; the phenomena ground the theory’s acceptance. Likewise, the general equations do not demonstrate the law of supply and demand; equations representing the chief phenomena of supply and demand are proven by experience.
A fifth argument concerns terminology. Science would gain by developing its own terminology, as chemistry, physics, and anatomy have done. Many criticisms of Pareto’s choice of terms are of absolutely no value, because they mistake words for things. Whether a ship is called capital depends not on any objective quality of the ship but on the way it is used in the process of production; the same thing can be considered as capital or not, according to how the balance sheet is drawn up. The dispute over “factors of production” versus “coefficients of industry” is a quarrel about words: it amounts to the same thing to say that four hectares yield eighty hectolitres of corn or that one-twentieth of a hectare yields one hectolitre. Pareto’s impatience with these disputes is not mere irritation; it expresses a methodological principle, that scientific progress depends on reasoning about things rather than about names.
A sixth argument, stated at the close, concerns the proper questions of economic science. Science does not attempt to establish any particular method of economic organization; that is not its business. It attempts to solve problems of the kind: what are the effects of free competition, of monopoly, of a collectivist regime? These questions must be treated not polemically but scientifically, as questions about the consequences of given arrangements.
Key Concepts
Several concepts organize the essay. The distinction between art and science is fundamental: art aims at persuasion and must be understood by those it addresses; science aims at truth and may use any instrument, however technical, that discloses it. The distinction between pure and applied science follows from this: pure science is not to be judged by its immediate utility, and the investigator is entitled to pursue a question as far as the science’s resources permit.
The concept of approximation is central to Pareto’s account of economic theory. Rational mechanics gives a first approximation to the concrete mechanical phenomenon; the theories of Jevons, Walras, Marshall, Fisher, and others give a first approximation to the full theory of economic phenomena. Pure economics can no more express the concrete economic phenomenon than rational mechanics can represent the concrete mechanical one. The approximation is rough but better than nothing—better to know the earth is nearly round than to imagine it flat.
The concept of mutual dependence is the reason mathematics is needed. Economists insist verbally that economic phenomena depend on one another, but only a system of equations can determine approximately the relations among them. Walras’s general system of equations expressing economic equilibrium is the model of this approach. Pareto’s own extension of the static equations to dynamic questions aims at the most accurate description of economic phenomena, and he finds it remarkable that a system of equations can express both the general character and every detail of economic phenomena, binding economic theory into an integral whole.
The concept of ophelimity—marginal utility—appears in the distinction between the consumer’s reckoning and the entrepreneur’s. Consumers reckon in marginal utility or ophelimity, while the entrepreneur counts in money; some criticisms might have been unnecessary had this distinction been noted. The concept of the coefficient of production, and its variability, leads to the function of entrepreneurs and to theories of different systems of production under free competition, monopoly, or a socialistic regime. The concept of the facility with which savings can be turned into different species of capital leads to a rigorous theory of rent. The concept of vibration—the economic aggregate vibrating under stimulating forces—leads to a theory of crises.
The concept of capital is treated as a matter of accounting convenience rather than objective quality. To be capital is not to possess an objective quality analogous to specific weight or chemical constitution; it is a characteristic which depends upon the way we use a thing in the process of production. The same thing can be considered as capital or not, according to how the balance sheet is drawn up. The concept of the budget of the producer is the base of calculations regarding production; the equations of production only formulate facts of the character gathered from such a budget.
Finally, the concept of verification: deductions must be compared with experience, not to prove the facts but to test the hypotheses and the presentation. The only adequate demonstration of political economy’s propositions is experience.
Themes
The dominant theme of the essay is the autonomy of science. Pareto returns repeatedly to the idea that science has its own standards, its own instruments, and its own questions, and that these are not to be subordinated to the demands of persuasion, reform, or moral edification. The theme is developed through the contrast between art and science, through the refusal to debate the utility of pure science, through the defense of mathematics as an instrument for complicated problems, and through the closing statement that science does not attempt to establish any particular method of economic organization. The essay can be read as a manifesto for a value-free economics, written at a time when such a stance was still contested.
A second theme is the relation between theory and observation. Pareto insists that the general equations rest on hypotheses, and that the deductions drawn from them must be compared with experience. But he also insists that facts cannot be demonstrated; they must be observed. The comparison of deduction with fact is a test of the theory, not a proof of the fact. This theme is developed through the analogy with the theory of undulations and the phenomena of interference, and through the rebuttal of critics who imagine that Pareto is trying to prove the law of supply and demand by deduction.
A third theme is the importance of terminology and the danger of verbal disputes. Pareto argues that science would gain by developing its own terminology, and that many criticisms of his work are quarrels about words. The example of capital and the example of factors of production versus coefficients of industry are used to show that the same facts can be described in different terms without any difference in the results. The theme is not merely linguistic; it expresses the view that scientific progress depends on reasoning about things rather than about names.
A fourth theme is the continuity of economics with the natural sciences. Pareto repeatedly draws analogies from mechanics, astronomy, chemistry, physics, anatomy, and philology. The problem of pure economics closely resembles that of rational mechanics; the separation of economic questions from legal questions is compared to the separation of chemistry from physics; the verification of economic deductions is compared to the verification of a calculating machine. The theme expresses a conception of economics as one science among others, sharing their methods and their standards.
A fifth theme, present throughout but especially in the closing pages, is the sociology of criticism. Pareto is interested in why critics misunderstand the new theories, and he offers explanations: the transition period in which works written according to new methods are judged by old principles; the tendency to measure science by the standards of art; the failure to read the book one criticizes. The theme gives the essay its polemical edge and its occasional tone of exasperation.
The Author’s Conclusions
Pareto concludes that the new economic theories, and the mathematical method they employ, are legitimate and necessary instruments for the scientific study of economic phenomena. The theories of Jevons, Walras, Marshall, Fisher, and others give a first approximation to the full theory of economic phenomena, just as rational mechanics gives a first approximation to the concrete mechanical one. The approximation is rough, but it is better than nothing, and it is the best that science can do at present.
He concludes that the mathematical method is justified not by greater rigor but by its capacity to handle complicated problems. The mutual dependence of economic phenomena can be acknowledged verbally by anyone, but only a system of equations can determine approximately the relations among phenomena and give a clear conception of their interdependence. Walras’s general system of equations expressing economic equilibrium is the great achievement of this approach, and Pareto’s own extension of the static equations to dynamic questions carries the work further.
He concludes that the general equations rest on hypotheses, and that the deductions drawn from them must be compared with experience. The comparison is not a demonstration of the facts but a test of the hypotheses and of the presentation. Critics who imagine that Pareto is trying to prove the facts by deduction have misunderstood the logic of the method. The only adequate demonstration of political economy’s propositions is experience.
He concludes that many criticisms of his terminology are of absolutely no value, because they mistake words for things. Whether a thing is called capital depends not on any objective quality but on the way it is used in the process of production. The dispute over factors of production versus coefficients of industry is a quarrel about words. Science would gain by developing its own terminology, as chemistry, physics, and anatomy have done.
He concludes, finally, that science does not attempt to establish any particular method of economic organization. Its business is to solve problems of the kind: what are the effects of free competition, of monopoly, of a collectivist regime? These questions must be treated not polemically but scientifically. The essay ends on this note of scientific neutrality, with the implication that the investigator’s task is to determine consequences, not to recommend arrangements.
Significance
The essay is significant as a statement of method by one of the founders of mathematical economics. It gives a clear and compact account of what Pareto believed he was doing in the Cours d’économie politique, and of why he believed the mathematical method was necessary. It also gives a vivid picture of the reception of the new theories in the late nineteenth century, and of the kinds of objection their proponents faced: that mathematics was unnecessary machinery for grinding out truisms, that it was inaccessible to the ordinary reader, that it had no power to encourage or discourage social reform, that its terminology was arbitrary and confusing. Pareto’s replies to these objections are of interest both as a defense of his own work and as a document in the history of economic thought.
The essay is also significant for its articulation of a value-free conception of economic science. Pareto’s insistence that science does not attempt to establish any particular method of economic organization, and that questions about the effects of free competition, monopoly, and collectivism must be treated scientifically rather than polemically, anticipates later debates about the role of the economist in public life. His refusal to debate the utility of pure science, and his defense of the investigator’s right to pursue a question as far as the science’s resources permit, express a conception of scientific autonomy that remains contested.
Finally, the essay is significant for its treatment of the relation between theory and observation. Pareto’s insistence that deductions must be compared with experience, but that facts cannot be demonstrated, and that the comparison serves to test hypotheses rather than to prove facts, is a clear statement of a methodological position that would become central to the philosophy of science. The analogies with the theory of undulations and with the calculating machine are memorable illustrations of the point. The essay’s closing questions—what are the effects of free competition, of monopoly, of a collectivist regime?—define an agenda for economic science that Pareto himself would pursue in later work, and that remains recognizable in the discipline today.
